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E-grāmata: Sentinel Method and Its Application to Environmental Pollution Problems

  • Formāts: 224 pages
  • Sērija : Mathematical Modeling
  • Izdošanas datums: 21-Jul-2023
  • Izdevniecība: CRC Press Inc
  • Valoda: eng
  • ISBN-13: 9780429612596
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Sentinel Method and Its Application to Environmental Pollution ProblemsPalielināt
  • Formāts: 224 pages
  • Sērija : Mathematical Modeling
  • Izdošanas datums: 21-Jul-2023
  • Izdevniecība: CRC Press Inc
  • Valoda: eng
  • ISBN-13: 9780429612596
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Introduces a new technique for solving problems in which some of the initial and/or boundary conditions are unknown, and shows how it can be applied to inverse problems of environmental pollution underground and in surface waters, and thermal and air pollution. The sentinel method is an implementation of the least-squares method particularly well adapted to identifying parameters in distributed ecosystems. Annotation c. by Book News, Inc., Portland, Or.

Many environmental problems contain incomplete data in the initial or boundary conditions. How do we solve problems for which some of the initial and/or boundary conditions are unknown? Using a new technique, the sentinel method, this book answers these questions and others as they pertain to inverse problems in environmental pollution, such as pollution of underground and surface waters, thermal pollution, and air pollution.

Many environmental problems contain incomplete data in the initial or boundary conditions
Notations
Introduction
1 Identification of pollution in an aquifer
1(22)
1.1 Modelling pollution transport in an aquifer
1(5)
1.2 A sentinel attached toeach parameter
6(5)
1.3 Examples of similar problems
11(4)
1.4 Flow rate
15(4)
1.5 Numerical experiments
19(1)
1.6 Sentinels and pseudo-inverse
20(3)
2 Identification of pollution in a lake
23(36)
2.1 Pollution of a lake
23(5)
2.2 Sentinels
28(10)
2.3 Numerical experiment
38(3)
2.4 Adjoint state
41(7)
2.5 Numerical details
48(2)
2.6 Hum method
50(2)
2.7 Time and space discretization
52(3)
2.8 Optimal emplacement of sensors
55(4)
3 Rectangular domain
59(22)
3.1 Physical motivations
59(1)
3.2 Modeling the physical system
60(1)
3.3 Exact solution of the direct problem
61(8)
3.4 Sentinels for inversion
69(1)
3.5 Direct method
70(1)
3.6 Numerical experiments
71(8)
3.7 Sensitivity to the size of the observatory
79(2)
4 Sentinels in a river
81(16)
4.1 Oxygen kinetics and polluted water
81(3)
4.2 Convection-dispersion-reaction equation
84(1)
4.3 Exact solution of state equation
85(4)
4.4 Sentinels for a river (evolution regime)
89(1)
4.5 Numerical experiments
90(7)
5 Our first nonlinear problem
97(28)
5.1 Linear case
97(10)
5.2 Nonlinear case
107(18)
6 Nonlinear problems
125(10)
6.1 Position of the problem
125(2)
6.2 Sentinels of the linearized problem
127(1)
6.3 Buliding the generalized inverse
128(1)
6.4 Example
129(6)
7 Dispersion coefficients
135(16)
7.1 Motivation
135(3)
7.2 Linearized system
138(2)
7.3 Linearized system sentinels
140(2)
7.4 Nonlinear problem
142(2)
7.5 Numerical results
144(7)
8 Position of a source
151(18)
8.1 Position of the problem
152(1)
8.2 Linearization
153(1)
8.3 Sentinels of the linearized problem
154(1)
8.4 Nonlinear problem
155(1)
8.5 Numerical experiments
156(2)
8.6 Unknown position and flow rate
158(2)
8.7 Sentinels of the linearized problem
160(2)
8.8 Sentinels of the linearized problem
162(1)
8.9 Moving source
162(7)
9 Recapitulation
169(10)
9.1 Definitions
169(2)
9.2 Inverse problems
171(2)
9.3 A convergence result
173(3)
9.4 Gauss-Newton method
176(3)
10 Shallow waters
179(8)
10.1 The movement of tides
179(3)
10.2 Numerical solution of shallow water equations
182(1)
10.3 Weak formulation
182(1)
10.4 Reaction-convection-dispersion equations
182(2)
10.5 Sentinels
184(3)
A Appendix: 187(10)
A.1 Sentinels with a given sensitivity 187(3)
A.2 Duality 190(4)
A.3 Existence of a solution and functional spaces 194(3)
References 197
Index 177
Jean-Pierre Kernévez
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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